An empirical mean-field model of symmetry-breaking in a turbulent wake

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Abstract

Improved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be disentangled from small-scale fluctuations. This closure problem is emblematic of a greater challenge in complex systems, where coarse-graining and statistical mechanics descriptions break down. This work demonstrates an alternative data-driven modeling approach to learn nonlinear models of the coherent structures, approximating turbulent fluctuations as state-dependent stochastic forcing. We demonstrate this approach on a high–Reynolds number turbulent wake experiment, showing that our model reproduces empirical power spectra and probability distributions. The model is interpretable, providing insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a path toward low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems.

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Callaham, J. L., Rigas, G., Loiseau, J. C., & Brunton, S. L. (2022). An empirical mean-field model of symmetry-breaking in a turbulent wake. Science Advances, 8(19). https://doi.org/10.1126/sciadv.abm4786

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